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I don't see the benefit of starting with acceleration as opposed
to, for example, mass. Once you have persuaded your students to
differentiate mass from weight, then weight per unit mass (as a proxy for
F/m) can follow directly. It is inntuitively and experienbtially obvious
that it is harder to push a truck, than a wheelbarrow - the essential
difference is mass, not weight. The notion of field is not necessary at
this point, so I don't see that F/m is all that difficult.